Liao, J., Xi, X., Bearup, D. and Sun, S. (2020). Metacommunity robustness of plant–fly–wasp tripartite networks with specialization to habitat loss. Ecology [Online]. Available at: https://doi.org/10.1002/ecy.3071.
Recent observations have found plant‐species‐specific fly‐host selection (i.e., specialization) of wasp parasitoids (wasps) in plant–fly–wasp (P–F–W) tripartite networks, yet no study has explored the dynamical implications of such high‐order specialization for the persistence of this network. Here we develop a patch‐dynamic framework for a unique P–F–W tripartite network with specialization observed in eastern Tibetan Plateau and explore its metacommunity robustness to habitat loss. We show that specialization in parasitoidism promotes fly species diversity, while the richness of both plant and wasp decreases. Compared to other two null models, real network structure favors plant species coexistence but increases the extinction risk for both flies and wasps. However, these effects of specialization and network structure would be weakened and ultimately disappear with increasing habitat loss. Interestingly, intermediate levels of habitat loss can maximize the diversity of flies and wasps, while increasing or decreasing habitat loss results in more species losses, supporting intermediate disturbance hypothesis. Finally, we observe that high levels of habitat loss initiate a bottom‐up cascade of species extinction from plants to both flies and wasps, resulting in a rapid collapse of the whole tripartite networks. Overall, this theoretical framework is the first attempt to characterize the dynamics of whole tripartite metacommunities interacting in realistic high‐order ways, offering new insights into complex multipartite networks.
Ma, C., Shen, Y., Bearup, D., Fagan, W. and Liao, J. (2020). Spatial variation in branch size promotes metapopulation persistence in dendritic river networks. Freshwater Biology [Online] 65:426-434. Available at: http://dx.doi.org/10.1111/fwb.13435.
1. Despite years of attention, the dynamics of species constrained to disperse within riverine networks are not well captured by existing metapopulation models, which often ignore local dynamics within branches. 2. We develop a modelling framework, based on traditional metapopulation theory, for occupancy dynamics subject to local colonization-extinction dynamics within branches and directional dispersal between branches in size-structured, bifurcating riverine networks. Using this framework, we investigate whether and how spatial variation in branch size affects species persistence for dendritic systems with directional dispersal. 3. Variation in branch size generally promotes species persistence more obviously at higher relative extinction rate, suggesting that previous studies ignoring differences in branch size in real riverine systems might overestimate species extinction risk. 4. Two-way dispersal is not always superior to one-way dispersal as a strategy for metapopulation persistence especially at high relative extinction rate. The type of dispersal which maximizes species persistence is determined by the hierarchical level of the largest, and hence most influential, branch within the network. When considering the interactive effects of up- and down-stream dispersal, we find that moderate upstream-biased dispersal maximizes metapopulation viability, mediated by spatial branch arrangement. 5. Overall, these results suggest that both branch-size variation and species traits interact to determine species persistence, theoretically demonstrating the ecological significance of their interplay.
Liao, J., Bearup, D. and Fagan, W. (2020). The role of omnivory in mediating metacommunity robustness to habitat destruction. Ecology [Online]. Available at: https://doi.org/10.1002/ecy.3026.
Omnivores have long been known to play an important role in determining the stability of ecological communities. Recent theoretical studies have suggested that they may also increase the resilience of their communities to habitat destruction, one of the major drivers of species extinctions globally. However, these outcomes were obtained for minimal food webs consisting of only a single omnivore and its prey species, while much more complex communities can be anticipated in nature. In this study, we undertake a systematic comparative analysis of the robustness of metacommunities containing various omnivory structures to habitat loss and fragmentation using a mathematical model. We observe that, in general, omnivores are better able to survive facing habitat destruction than specialist predators of similar trophic level. However, the community as a whole does not always benefit from the presence of omnivores, as they may drive their intraguild prey to extinction. We also analyze the frequency with which these modules occur in a set of empirical food webs, and demonstrate that variation in their rate of occurrence is consistent with our model predictions. Our findings demonstrate the importance of considering the complete food web in which an omnivore is embedded, suggesting that future study should focus on more holistic community analysis.
Chen, D., Liao, J., Bearup, D. and Li, Z. (2020). Habitat heterogeneity mediates effects of individual variation on spatial species coexistence. Proceedings of the Royal Society B: Biological Sciences [Online] 287. Available at: https://doi.org/10.1098/rspb.2019.2436.
Numerous studies have documented the importance of individual variation (IV) in determining the outcome of competition between species. However, little is known about how the interplay between IV and habitat heterogeneity (i.e. variation and spatial autocorrelation in habitat quality) affects species coexistence at the landscape scale. Here, we incorporate habitat heterogeneity into a competition model with IV, in order to explore the mechanism of spatial species coexistence. We find that individual-level variation and habitat heterogeneity interact to promote species coexistence, more obviously at lower dispersal rates. This is in stark contrast to early non-spatial models, which predicted that IV reinforces competitive hierarchies and therefore speeds up species exclusion. In essence, increasing variation in patch quality and/or spatial habitat autocorrelation moderates differences in the competitive ability of species, thereby allowing species to coexist both locally and globally. Overall, our theoretical study offers a mechanistic explanation for emerging empirical evidence that both habitat heterogeneity and IV promote species coexistence and therefore biodiversity maintenance.
Bearup, D., Childs, D. and Freckleton, R. (2018). Funder Restrictions on Application Numbers Lead to Chaos. Trends in Ecology and Evolution [Online] 33:565-568. Available at: https://doi.org/10.1016/j.tree.2018.06.001.
Restricting application rates is an attractive way for funders to reduce time and money wasted
evaluating uncompetitive applications. However, mathematical models show that this could
induce chaotic cycles in total application numbers, increasing uncertainty in the funding
process. One emergent property is that smaller institutions spend disproportionally more time
Liao, J., Bearup, D. and Blasius, B. (2017). Food web persistence in fragmented landscapes. Proceedings of the Royal Society B: Biological Sciences [Online] 284. Available at: https://royalsocietypublishing.org/doi/10.1098/rspb.2017.0350.
Habitat destruction, characterized by patch loss and fragmentation, is a key driver of biodiversity loss. There has been some progress in the theory of spatial food webs; however, to date, practically nothing is known about how patch configurational fragmentation influences multi-trophic food web dynamics. We develop a spatially extended patch-dynamic model for different food webs by linking patch connectivity with trophic-dependent dispersal (i.e. higher trophic levels displaying longer-range dispersal). Using this model, we find that species display different sensitivities to patch loss and fragmentation, depending on their trophic position and the overall food web structure. Relative to other food webs, omnivory structure significantly increases system robustness to habitat destruction, as feeding on different trophic levels increases the omnivore’s persistence. Additionally, in food webs with a dispersal–competition trade-off between species, intermediate levels of habitat destruction can enhance biodiversity by creating refuges for the weaker competitor. This demonstrates that maximizing patch connectivity is not always effective for biodiversity maintenance, as in food webs containing indirect competition, doing so may lead to further species loss.
Liao, J., Bearup, D. and Blasius, B. (2017). Diverse responses of species to landscape fragmentation in a simple food chain. Journal of Animal Ecology [Online] 86:1169-1178. Available at: http://dx.doi.org/10.1111/1365-2656.12702.
1) Habitat destruction, characterized by habitat loss and fragmentation, is a key driver of species extinction in spatial extended communities. Recently, there has been some progress in the theory of spatial food webs, however to date practically little is known about how habitat configurational fragmentation influences multi-trophic food web dynamics.
2) To explore how habitat fragmentation affects species persistence in food webs, we introduce a modelling framework that describes the site occupancy of species in a tri-trophic system. We assume that species dispersal range increases with trophic level, exploiting pair-approximation techniques to describe the effect of habitat clustering.
3) In accordance with the trophic rank hypothesis, both habitat loss and fragmentation generally cause species extinction, with stronger effects occurring at higher trophic levels. However, species display diverse responses (negative, neutral or positive) to habitat loss and fragmentation separately, depending on their dispersal range and trophic position.
4) Counter-intuitively, prey species may benefit from habitat loss due to a release in top-down control. Similarly, habitat fragmentation has almost no influence on the site occupancy of the intermediate consumer in the tri-trophic system, though it decreases those of both basal species and top predator. Consequently, species’ responses to habitat destruction vary as other species become extinct.
5) Our results reiterate the importance of the interplay between bottom-up and top-down control in trophically linked communities, and highlight the complex responses occurring in even a simple food chain.
Liao, J., Bearup, D., Wang, Y., Nijs, I., Bonte, D., Li, Y., Brose, U., Wang, S. and Blasius, B. (2017). Robustness of metacommunities with omnivory to habitat destruction: disentangling patch fragmentation from patch loss. Ecology [Online] 98:1631-1639. Available at: http://dx.doi.org/10.1002/ecy.1830.
Habitat destruction, characterized by patch loss and fragmentation, is a major driving force of species extinction, and understanding its mechanisms has become a central issue in biodiversity conservation. Numerous studies have explored the effect of patch loss on food web dynamics, but ignored the critical role of patch fragmentation. Here we develop an extended patch-dynamic model for a tri-trophic omnivory system with trophic-dependent dispersal in fragmented landscapes. We found that species display different vulnerabilities to both patch loss and fragmentation, depending on their dispersal range and trophic position. The resulting trophic structure varies depending on the degree of habitat loss and fragmentation, due to a tradeoff between bottom-up control on omnivores (dominated by patch loss) and dispersal limitation on intermediate consumers (dominated by patch fragmentation). Overall, we find that omnivory increases system robustness to habitat destruction relative to a simple food chain.
Bearup, D. and Blasius, B. (2017). Ecotone formation induced by the effects of tidal flooding: A conceptual model of the mud flat-coastal wetland ecosystem. Ecological Complexity [Online] 32:217-227. Available at: https://dx.doi.org/10.1016/j.ecocom.2016.11.005.
The boundary between mud flat and coastal wetland ecosystems is highly productive and a haven of considerable biodiversity. It is also embedded in a highly dynamic environment and can be easily destabilised by environmental changes, invasive species, and human activity. Thus, understanding the processes which govern the formation of this ecotone is important both for conservation and economic reasons. In this study we introduce a simple conceptual model for this joint ecosystem, which demonstrates that the interaction between tidal flooding and habitat elevation is able to produce an ecotone with similar characteristics to that observed in empirical studies. In particular, the transition from mud flat to vegetated state is locally abrupt, occurring at a critical threshold elevation, but, on broader spatial scales can occur over a range of elevations determined by the variability in high tide water levels. Additionally, the model shows the potential for regime shifts, resulting from periods of unusual weather or the invasion of a fast growing, or flood resistant, species.
Ritterskamp, D., Bearup, D. and Blasius, B. (2016). Emergence of evolutionary cycles in size-structured food webs. Journal of Theoretical Biology [Online] 408:187-197. Available at: http://dx.doi.org/10.1016/j.jtbi.2016.08.024.
The interplay of population dynamics and evolution within ecological communities has been of long-standing interest for ecologists and can give rise to evolutionary cycles, e.g. taxon cycles. Evolutionary cycling was intensely studied in small communities with asymmetric competition; the latter drives the evolutionary processes. Here we demonstrate that evolutionary cycling arises naturally in larger communities if trophic interactions are present, since these are intrinsically asymmetric. To investigate the evolutionary dynamics of a trophic community, we use an allometric food web model. We find that evolutionary cycles emerge naturally for a large parameter ranges. The origin of the evolutionary dynamics is an intrinsic asymmetry in the feeding kernel which creates an evolutionary ratchet, driving species towards larger bodysize. We reveal different kinds of cycles: single morph cycles, and coevolutionary and mixed cycling of complete food webs. The latter refers to the case where each trophic level can have different evolutionary dynamics. We discuss the generality of our findings and conclude that ongoing evolution in food webs may be more frequent than commonly believed.
Bearup, D., Benefer, C., Petrovskii, S. and Blackshaw, R. (2016). Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data. Methods in Ecology and Evolution [Online] 7:1525-1537. Available at: http://dx.doi.org/10.1111/2041-210X.12615.
1) Characterization of patterns of animal movement is a major challenge in ecology with applications to conservation, biological invasions and pest monitoring. Brownian random walks, and diffusive flux as their mean field counterpart, provide one framework in which to consider this problem. However, it remains subject to debate and controversy. This study presents a test of the diffusion framework using movement data obtained from controlled experiments.
2) Walking beetles (Tenebrio molitor) were released in an open circular arena with a central hole and the number of individuals falling from the arena edges was monitored over time. These boundary counts were compared, using curve fitting, to the predictions of a diffusion model. The diffusion model is solved precisely, without using numerical simulations.
3) We find that the shape of the curves derived from the diffusion model is a close match to those found experimentally. Furthermore, in general, estimates of the total population obtained from the relevant solution of the diffusion equation are in excellent agreement with the experimental population. Estimates of the dispersal rate of individuals depend on how accurately the initial release distribution is incorporated into the model.
4) We therefore show that diffusive flux is a very good approximation to the movement of a population of Tenebrio molitor beetles. As such, we suggest that it is an adequate theoretical/modelling framework for ecological studies that account for insect movement, although it can be context specific. An immediate practical application of this can be found in the interpretation of trap counts, in particular for the purpose of pest monitoring.
Ritterskamp, D., Feenders, C., Bearup, D. and Blasius, B. (2016). Evolutionary food web models: effects of an additional resource. Theoretical Ecology [Online] 9:501-512. Available at: http://dx.doi.org/10.1007/s12080-016-0305-0.
Many empirical food webs contain multiple resources, which can lead to the emergence of sub-communities—partitions—in a food web that are weakly connected with each other. These partitions interact and affect the complete food web. However, the fact that food webs can contain multiple resources is often neglected when describing food web assembly theoretically, by considering only a single resource. We present an allometric, evolutionary food web model and include two resources of different sizes. Simulations show that an additional resource can lead to the emergence of partitions, i.e. groups of species that specialise on different resources. For certain arrangements of these partitions, the interactions between them alter the food web properties. First, these interactions increase the variety of emerging network structures, since hierarchical bodysize relationships are weakened. Therefore, they could play an important role in explaining the variety of food web structures that is observed in empirical data. Second, interacting partitions can destabilise the population dynamics by introducing indirect interactions with a certain strength between predator and prey species, leading to biomass oscillations and evolutionary intermittence.
Ritterskamp, D., Bearup, D. and Blasius, B. (2016). A new dimension: Evolutionary food web dynamics in two dimensional trait space. Journal of Theoretical Biology [Online] 405:66-81. Available at: https://doi.org/10.1016/j.jtbi.2016.03.042.
Species within a habitat are not uniformly distributed. However this aspect of community structure, which is fundamental to many conservation activities, is neglected in the majority of models of food web assembly. To address this issue, we introduce a model which incorporates a second dimension, which can be interpreted as space, into the trait space used in evolutionary food web models. Our results show that the additional trait axis allows the emergence of communities with a much greater range of network structures, similar to the diversity observed in real ecological communities. Moreover, the network properties of the food webs obtained are in good agreement with those of empirical food webs. Community emergence follows a consistent pattern with spread along the second trait axis occurring before the assembly of higher trophic levels. Communities can reach either a static final structure, or constantly evolve. We observe that the relative importance of competition and predation is a key determinant of the network structure and the evolutionary dynamics. The latter are driven by the interaction—competition and predation—between small groups of species. The model remains sufficiently simple that we are able to identify the factors, and mechanisms, which determine the final community state.
Bearup, D., Petrovskaya, N. and Petrovskii, S. (2015). Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration. Mathematical Biosciences [Online] 263:143-160. Available at: http://dx.doi.org/10.1016/j.mbs.2015.02.008.
Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. First, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called “activity-density” problem). Second, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth.
Bearup, D. and Petrovskii, S. (2014). On time scale invariance of random walks in confined space. Journal of Theoretical Biology [Online] 367:230-245. Available at: http://dx.doi.org/10.1016/j.jtbi.2014.11.027.
Animal movement is often modelled on an individual level using simulated random walks. In such applications it is preferable that the properties of these random walks remain consistent when the choice of time is changed (time scale invariance). While this property is well understood in unbounded space, it has not been studied in detail for random walks in a confined domain. In this work we undertake an investigation of time scale invariance of the drift and diffusion rates of Brownian random walks subject to one of four simple boundary conditions. We find that time scale invariance is lost when the boundary condition is non-conservative, that is when movement (or individuals) is discarded due to boundary encounters. Where possible analytical results are used to describe the limits of the time scaling process, numerical results are then used to characterise the intermediate behaviour.
Petrovskii, S., Petrovskaya, N. and Bearup, D. (2014). Multiscale ecology of agroecosystems is an emerging research field that can provide a stronger theoretical background for the integrated pest management. Reply to comments on "Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks". Physics of Life Reviews [Online] 11:536-539. Available at: http://dx.doi.org/10.1016/j.plrev.2014.07.001.
Petrovskii, S., Petrovskaya, N. and Bearup, D. (2014). Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks. Physics of Life Reviews [Online] 11:467-525. Available at: http://dx.doi.org/10.1016/j.plrev.2014.02.001.
Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agro-ecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scale-specific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation.
Bearup, D., Petrovskii, S., Blackshaw, R. and Hastings, A. (2013). Synchronized dynamics of Tipula paludosa metapopulation in a southwestern Scotland agroecosystem: Linking pattern to process. American Naturalist [Online] 182:393-409. Available at: http://dx.doi.org/10.1086/671162.
Synchronization of population fluctuations at disjoint habitats has been observed in many studies, but its mechanisms often remain obscure. Synchronization may appear as a result of either interhabitat dispersal or regionally correlated environmental stochastic factors, the latter being known as the Moran effect. In this article, we consider the population dynamics of a common agricultural pest insect, Tipula paludosa, on a fragmented habitat by analyzing data derived from a multiannual survey of its abundance in 38 agricultural fields in southwestern Scotland. We use cross-correlation coefficients and show that there is a considerable synchronization between different populations across the whole area. The correlation strength exhibits an intermittent behavior, such that close populations can be virtually uncorrelated, but populations separated by distances up to approximately 150 km can have a cross-correlation coefficient close to one. To distinguish between the effects of stochasticity and dispersal, we then calculate a time-lagged cross-correlation coefficient and show that it possesses considerably different properties to the nonlagged one. In particular, the time-lagged correlation coefficient shows a clear directional dependence. The distribution of the time-lagged correlations with respect to the bearing between the populations has a striking similarity to the distribution of wind velocities, which we regard as evidence of long-distance wind-assisted dispersal.
Bearup, D., Evans, N. and Chappell, M. (2012). The input-output relationship approach to structural identifiability analysis. Computer Methods and Programs in Biomedicine [Online] 109:171-181. Available at: http://dx.doi.org/10.1016/j.cmpb.2012.10.012.
Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of non-linear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The input–output relation of a model summarises the input–output structure of the whole system and as such provides the potential for an alternative approach to this analysis. However for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple. These techniques are applied to analyse classical models from biomedical systems modelling and those of enzyme catalysed reaction schemes.
Petrovskii, S., Bearup, D., Ahmed, D. and Blackshaw, R. (2011). Estimating insect population density from trap counts. Ecological Complexity [Online] 10:69-82. Available at: http://dx.doi.org/https://doi.org/10.1016/j.ecocom.2011.10.002.
Trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. Despite this, the interpretation of trap counts is challenging. Traps are effective at providing relative counts that enable comparisons but are poor at delivering information on the absolute population size. Making better use of trap data is impeded by the lack of a consistent underlying theoretical model. In this paper, we aim to overcome current limitations of trapping methods used in ecological studies through developing a theoretical and methodological framework that enables a direct estimate of populations from trap counts. We regard insect movement as stochastic Brownian motion and use two different mathematical approaches accordingly. We first use individual-based modelling to reproduce trap catch patterns and study the effect of individual movement on observed catch patterns. We then consider a ‘mean-field’ diffusion model and show that it is capable of revealing the generic relationship between trap catches and population density.
Hattersley, J., Pérez-Velázquez, J., Chappell, M., Bearup, D., Roper, D., Dowson, C., Bugg, T. and Evans, N. (2010). Indistinguishability and identifiability of kinetic models for the MurC reaction in peptidoglycan biosynthesis. Computer Methods and Programs in Biomedicine [Online] 104:70-80. Available at: https://doi.org/10.1016/j.cmpb.2010.07.009.
An important question in Systems Biology is the design of experiments that enable discrimination between two (or more) competing chemical pathway models or biological mechanisms. In this paper analysis is performed between two different models describing the kinetic mechanism of a three-substrate three-product reaction, namely the MurC reaction in the cytoplasmic phase of peptidoglycan biosynthesis. One model involves ordered substrate binding and ordered release of the three products; the competing model also assumes ordered substrate binding, but with fast release of the three products. The two versions are shown to be distinguishable; however, if standard quasi-steady-state assumptions are made distinguishability cannot be determined. Once model structure uniqueness is ensured the experimenter must determine if it is possible to successfully recover rate constant values given the experiment observations, a process known as structural identifiability. Structural identifiability analysis is carried out for both models to determine which of the unknown reaction parameters can be determined uniquely, or otherwise, from the ideal system outputs. This structural analysis forms an integrated step towards the modelling of the full pathway of the cytoplasmic phase of peptidoglycan biosynthesis.